Optimal and near-optimal manipulators joint trajectories with a preplanned path

Manipulator joint trajectories are planned to optimize a specified cost function under preplanned path constraints in consideration of physical constraints based on kinematics and dynamics of a manipulator system. Introducing a time scale factor k(t), all the sets of joint trajectories are described by a set of ones, called reference trajectories, k(t) and its time derivative k(t). The desirable k(t) is obtained by two proposed methods: the first one is a global optimization method using dynamic programming (DP) and the second one is the iteratively improving (II) method which is a feasible method and utilizes the local controllability of B-spline. These methods are applied of an example of the joint trajectory planning for a preplanned collision-free path of a manipulator. The numerical results point out that II method is much more effective than DP method in view of the computation time and memories, if the strictly optimal solution is not required.